Hopalong Orbits Visualizer: The Math Behind the Most Beautiful WebGL Experiment
Barry Martin's Hopalong attractor turns three lines of algebra into galaxy-like structures rendered in real-time 3D. Here's the mathematics behind…
Math
Mathematics Blog by Gaurav Tiwari. This section is dedicated to exploring various mathematical concepts and theories, transcending the boundaries of traditional high school and early college curriculums.
The mathematics topics here encompass various subfields, including algebra, calculus, number theory, geometry, topology, and more.
Real Sequences: Definitions, Theorems, and Examples
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and…
Euler’s (Prime to) Prime Generating Equation
Euler discovered a simple formula that generates 40 consecutive prime numbers: n squared plus n plus 41. Plug in 0…
Area of a Disk – Why is it πr²?
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…
Triangle Inequality: Concepts, Theorems, and Examples
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But…
National Mathematical Year 2012: What India Promised Ramanujan and What It Actually Delivered
In December 2011, India declared 2012 as National Mathematical Year to honor Ramanujan's 125th birthday. I wrote at the time…
The Quest for a Prime Number Formula: Why It’s Harder Than You Think
Mathematicians have spent centuries trying to find a formula that generates all prime numbers. Euler's n²+n+41 works for 40 values…
Find the Day of a Date using this Calendar Formula
You can figure out what day of the week any date falls on. No calendar needed. Just arithmetic. I'll teach…
Equations: A Basic Introduction
Equations are the reason we can solve problems in seconds that would take hours of guesswork. I cover the basics:…
Types of Numbers in Mathematics: Rational, Irrational, Real, and Complex Numbers
Numbers are the alphabet of mathematics. But here's what most people never learn: all the complex numbers you encounter, from…
Mathematical Logic: The Foundation Everything Else Builds On
Logic is the grammar of mathematics. Without logical precision, you can't communicate ideas or verify they're correct. Propositions, truth tables,…
Fermat Numbers (Important Theorems & Examples)
Fermat was convinced he'd found an infinite source of primes. He was wrong. His formula n^2 + n + 41…